h-norm index
Properties
- Metric Type: Core Metric
- Considerations and Adjustments: Coauthorship
- Publication Focus: Core Publications
- Citation Focus: Core Citations
Description
The h-norm index (Anania and Caruso 2013) is described more or less incidentally when building up to normalized versions of other metrics in the paper. It is a version of the h-index normalized by the number of coauthors for each publication. It is very similar to the calculation of he when determining the adapted pure h-index (fractional credit), but citation counts are divided by the number of coauthors rather than the square root. Citation accounts are adjusted for coauthor counts as:
$$C^{*}_i = \frac{C_i}{A_i}.$$and h-norm isdetermined using these adjusted counts:
$$h{-}norm = \underset{i}{\max}\left(i \leq C^{*}_i\right).$$Example
Publications are ordered by adjusted number of citations, from highest to lowest.
| Citations (Ci) | 59 | 11 | 26 | 16 | 11 | 3 | 10 | 4 | 1 | 1 | 3 | 2 | 1 | 0 | 0 | 0 | 0 | 0 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Authors (Ai) | 3 | 1 | 3 | 2 | 3 | 1 | 4 | 4 | 1 | 1 | 4 | 4 | 2 | 4 | 2 | 1 | 1 | 1 |
| Adjusted Citations (\(C^*_i\)) | 19.67 | 11.00 | 8.67 | 8.00 | 3.67 | 3.00 | 2.50 | 1.00 | 1.00 | 1.00 | 0.75 | 0.50 | 0.50 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| h-norm = 4 |
The largest rank where \(i \leq C^*_i\) is 4.
History
| Year | h-norm |
|---|---|
| 1997 | 0 |
| 1998 | 1 |
| 1999 | 2 |
| 2000 | 4 |
| 2001 | 4 |
| 2002 | 6 |
| 2003 | 8 |
| 2004 | 9 |
| 2005 | 12 |
| 2006 | 14 |
| 2007 | 16 |
| 2008 | 19 |
| 2009 | 20 |
| 2010 | 22 |
| 2011 | 23 |
| 2012 | 24 |
| 2013 | 26 |
| 2014 | 26 |
| 2015 | 26 |
| 2016 | 27 |
| 2017 | 27 |
| 2018 | 27 |
| 2019 | 28 |
| 2020 | 29 |
| 2021 | 31 |
| 2022 | 33 |
| 2023 | 33 |
| 2024 | 33 |
| 2025 | 33 |
References
- Anania, G., and A. Caruso (2013) Two simple new bibliometric indexes to better evaluate research in disciplines where publications typically receive less citations. Scientometrics 96:617-631.